Non-instantaneous impulsive Hilfer fractional stochastic differential equations driven by fractional Brownian motion. Issue 3 (4th May 2021) - Saravanakumar, S.; Balasubramaniam, P.
Abstract: The aim of this manuscript is to analyze the existence of mild solution of non-instantaneous impulsive Hilfer fractional stochastic differential equations (NIHFSDEs) driven by fractional Brownian motion (fBm). Sufficient conditions for a class of NIHFSDEs of order 0 < β < 1 and of type 0 ≤ α ≤ 1 driven by fBm is derived with the help of fractional calculus, stochastic theory, fixed point theorem and semigroup theory. M ö nch fixed point theorem (FPT) is adopted to prove the existence of solution. In addition, a numerical example is provided to validate the theoretical result.